In order to make high data rate interactive services such as video and internet access available to more residential and small business customers, high-speed data communications paths are required. Although fiber optic cable is the preferred transmission media for such high data rate services, it is not readily available in existing communication networks and the expense of installing fiber optic cabling is prohibitive. Current telephone wiring connections, which consist of copper twisted-pair media, were not originally designed to support the data rates or bandwidth required for interactive services such as video on demand or even high speed internet connections. Asymmetric Digital Subscriber Line (ADSL) technology has been developed to increase the effective bandwidth of existing twisted-pair connections, allowing interactive services to be provided without requiring the installation of fiber optic cable.
Discrete multi-tone (DMT) is a multi-carrier technique which divides the available bandwidth of twisted-pair copper media connections into mini-subchannels or bins. The DMT technique has been adopted in the ANSI T1.413 standard (ADSL standard). In the ADSL standard, DMT is used to generate 250 separate 4.3125 kilohertz subchannels from 26 kilohertz to 1.1 megahertz for downstream transmission to an end user. Likewise, DMT is used to generate 26 subchannels from 26 kilohertz to 138 kilohertz for upstream transmission by an end user.
In the ADSL system, changing channel conditions require adaptive equalizers to improve the signal-to-noise ratio (SNR) of the received signal. A Fast Fourier Transform (FFT) module is used to convert a received time domain signal to the frequency domain. The equalization is performed in the frequency domain on individual carriers of a transmission using DMT. Each of the carriers which make up the DMT symbol contains a single quadrature amplitude modulated (QAM) signal, and is equalized using a one-tap equalizer which is updated independent from each of the other carriers.
For example, FIG. 1 illustrates, in graphical form, a signal constellation of a frequency domain signal which is subjected to phase and amplitude errors. The horizontal axis is the real part and the vertical axis is the imaginary part. The dots, one of which is labeled "X.sub.EST (k)", indicate the desired frequency domain signal in vector format, and the Xs, one of which is labeled "X(k)", indicate the received frequency domain signal. For purposes of simplicity and clarity, the signal constellation of FIG. 1 is illustrated with only one signal per quadrant. Other signal constellations may have more or fewer signals in each of the four quadrants. A calculated error term labeled "E(k)" is indicated as a vector between the desired frequency domain signal and the received frequency domain signal. In FIG. 1, there is no phase or amplitude imbalance, so the calculated error term has the same relative amplitude and phase relationship for each quadrant.
Equalization is performed on the signal constellation of FIG. 1 using the least mean squares (LMS) algorithm and requires complex multiplies to compute the coefficient updates. Adaptive updates are performed using the following equation: EQU W(k)=W(k-1)+2.mu.E(k)X*.sub.EST (k) (1)
where:
W(k)=equalizer coefficient at time k; PA1 2.mu.=adaptation constant; PA1 E(k)=calculated error term; and PA1 X*.sub.EST (k)=conjugate of received data estimate.
In a DMT system with a large number of carriers, performing equalization using the above equation to calculate the coefficients can result in a large number of calculations. What is needed, then, is a method for performing the equalization function which reduces the number of required calculations. Such a method and an equalizer using this method are provided by the present invention, whose features and advantages will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings.